Question

A 75-turn coil with a diameter of 6.00 cm is placed in a constant, uniform magnetic field of 1.00 T directed perpendicular to the plane of the coil. Beginning at time t = 0 s, the field is increased at a uniform rate until it reaches 1.30 T at t = 10.0 s. The field remains constant thereafter. What is the magnitude of the induced emf in the coil at the t=5s?

Answer 1

Answer:

The induced emf in the coil at the t = 5s is 6.363 mV

Explanation:

Given;

number of turns = 75

diameter of the coil = 6 cm

magnetic field strength = 1 T

new magnetic field strength = 1.30 T at t = 10.0 s

$Area \ of \ coil = \frac{\pi d^2}{4} = \frac{\pi *0.06^2}{4} = 0.002828 \ m^2$

$E.M.F = \frac{NA* \delta B}{\delta t}$

Between 0 to 5 s, Induced emf is given as;

$E.M.F = \frac{75*0.002828*(B_5-1)}{5}$

Between 5 to 10 s, Induced emf is given as;

$E.M.F = \frac{75*0.002828*(1.3-B_5)}{5}$

Since the field increased at a uniform rate until it reaches 1.30 T at t = 10.0 s, the induced emf will also increase in uniform rate. And equal time interval will generate same increase in field strength.

B₅ -1 = 1.3 - B₅

2B₅ = 2.3

B₅ = 1.15 T

Thus, magnetic field at t = 5 is 1.15 T

$E.M.F = \frac{75*0.002828*(1.3-1.15)}{5} = 6.363 \ mV$

Therefore, the induced emf in the coil at the t = 5s is 6.363 mV